Knowing Our Numbers

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NCERT Solutions for Chapter 1 Knowing Our Numbers Class 6 Maths

Book Solutions

1

Fill in the blanks: 
(a) 1 lakh = _______ ten thousand.
(b) 1 million = _______ hundred thousand. 
(c) 1 crore = _______ ten lakh. 
(d) 1 crore = _______ million. 
(e) 1 million = _______ lakh

Answer

a) 100
b) 10
c) 10
d) 10
e) 100
Exercise 1.1 Page Number 11

2

Place commas correctly and write the numerals:
(a) Seventy three lakh seventy five thousand three hundred seven.
(b) Nine crore five lakh forty one.
(c) Seven crore fifty two lakh twenty one thousand three hundred two. 
(d) Fifty eight million four hundred twenty three thousand two hundred two.
(e) Twenty three lakh thirty thousand ten.

Answer

a) 73,75,307
b) 9,05,000,41
c) 7,52,21,302
d) 58,423,202
e) 23,30,010
Exercise 1.1 Page Number 11

3

Insert commas suitably and write the names according to Indian System of Numeration: 
(a) 87595762
(b) 8546283
(c) 99900046 
(d) 98432701

Answer

(a) 8,75,95,762: Eight crore seventy five lakh ninety five seven hundred sixty two.
(b) 85,46,283: Eighty five lakh forty six thousand two hundred eighty three
(c) 9,99,00,046: Nine crore ninety nine lakh forty six
(d) 9,84,32,701: Nine crore eighty four lakh thirty two thousand seven hundred one.
Exercise 1.1 Page Number 11

4

Insert commas suitably and write the names according to International System of Numeration:
(a) 78921092 
(b) 7452283 
(c) 99985102 
(d) 48049831

Answer

(a) 78,921,092: Seventy eight million nine hundred twenty one thousand ninety two.
(b) 7,452,283: Seven million four hundred fifty two thousand two hundred eighty three.
(c) 99,985,102: Ninety nine million nine hundred eighty five thousand one hundred two.
(e) 48,049,831: Forty eight million forty nine thousand eight hundred thirty one.
Exercise 1.1 Page Number 11

1

A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

Answer

Number of tickets sold on first day = 1,094

Number of tickets sold on second day = 1,812

Number of tickets sold on third day = 2,050

Number of tickets sold on fourth day = 2,751

Total Number of tickets sold = 1094 + 1812 + 2050 + 2751 = 7,707

Therefore, 7,707 tickets were sold on all the four days.

Exercise 1.2 Page Number 15

2

Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?

Answer

Runs to achieve = 10,000

Runs scored = 6,980

Runs required = 10,000 - 6980 = 3,020

Therefore, Shekar needs 3,020 more runs.

Exercise 1.2 Page Number 15

3

In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?

Answer

Number of votes secured by successful candidates = 5,77,500

Number of votes secured by his nearest rival =  3,48,700

Margin between them = 5,77,500 - 3,48,700 = 2,28,800

Therefore, the successful candidate won by a margin of 2,28,800 votes.

Exercise 1.2 Page Number 15

4

Kirti Bookstore sold books worth 2,85,891 in the first week of June and books worth 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Answer

Books sold in first week = 2,85,891

Books sold in second week = 4,00,768

Total books sold = 2,85,891 + 4,00,768 = 6,86,659

Since, 4,00,768 > 2,85,891

Therefore sale of second week is greater than that of first week.

Books sold in second week = 4,00,768

Books sold in first week = 2,85,891

More books sold in second week =  4,00,768 - 2,85,891 = 1,14,877

Therefore, sale in second week was larger than sale in first week by 1,14,877 

Exercise 1.2 Page Number 15

5

Find the difference between the greatest and the least number that can be written using the digits 6, 2, 7, 4, 3 each only once.

Answer

Greatest five-digit number using digits 6,2,7,4,3 = 76432

Smallest five-digit number using digits 6,2,7,4,3 = 23467

Difference = 76432 - 23467= 52965

Therefore the difference is 52965.

Exercise 1.2 Page Number 16

6

A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

Answer

Number of screws manufactured in one day = 2,825

Number of days in the month of January (31 days) = 2,825 x 31

Therefore the machine produced 87,575 screws in the month of January.

Exercise 1.2 Page Number 16

7

A merchant had 78,592 with her. She placed an order for purchasing 40 radio sets at 1,200 each. How much money will remain with her after the purchase?

Answer

Cost of one radio = 1200

Cost of 40 radios = 1200 x 40 = 48,000

Now, Total money with merchant = 78,592

Money spent by her = 48,000

Money left with her = 78,592 - 40,000 = 30,592

Therefore, Rs 30,592 will remain with her after the purchase.

Exercise 1.2 Page Number 16

8

A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?

Answer

Wrong answer = 7236 x 65

Correct answer = 7236 x 56

Difference in answers = 470340 – 405216 = 65,124
Exercise 1.2 Page Number 16

9

To stitch a shirt 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?

Answer

: Cloth required to stitch one shirt = 2 m 15 cm

= 2 x 100 cm + 15 cm = 215 cm

Length of cloth = 40 m = 40 x 100 cm = 4000 cm

Number of shirts can be stitched = 4000 ÷ 215

Therefore, 18 shirts can be stitched and 130 cm (1 m 30 cm) cloth will remain.

Exercise 1.2 Page Number 16

10

Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a can which cannot carry beyond 800 kg?

Answer

The weight of one box = 4 kg 500 g = 4 x 1000 g + 500 g = 4500 g

Maximum load can be loaded in van = 800 kg = 800 x 1000 g = 800000 g

Number of boxes = 800000 ÷ 4500

Therefore, 177 boxes can be loaded.

Exercise 1.2 Page Number 16

11

The distance between the school and the house of a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

Answer

Distance between school and home = 1.875 km
Distance between home and school = + 1.875 km
Total distance covered in one day = 3.750 km
Distance covered in six days = 3.750 x 6 = 22.500 km
Therefore, 22 km 500 m distance covered in six days.
Exercise 1.2 Page Number 16

12

A vessel has 4 liters and 500 ml of curd. In how many glasses each of 25 ml capacity, can it be filled?

Answer

: Capacity of curd in a vessel = 4 liters 500 ml = 4 x 1000 ml + 500 ml = 4500 ml
Capacity of one glass = 25 ml
Number of glasses can be filled = 4500 ÷" role="presentation" id="MathJax-Element-11-Frame" style="-webkit-tap-highlight-color: transparent; overflow-wrap: normal; max-width: none; max-height: none; min-width: 0px; min-height: 0px; float: none; word-spacing: normal;">÷ 25

Therefore, 180 glasses can be filled by curd.

Exercise 1.2 Page Number 16

1

Estimate each of the following using general rule:

(a) 730 + 998

(b) 796 – 314

(c) 12,904 + 2,888

(d) 28,292 – 21,496

Answer

(a) 730 + 998

By rounding off to nearest hundreds, 730 rounds off to 700 and 998 rounds off to 1000

Estimated sum = 700 + 1000 = 1700

(b) 796 - 314

By rounding off to nearest hundreds, 796 rounds off to 800 and 314 rounds off to 300

Estimated difference = 800 - 300 = 500

(c) 12,904 + 2,888

By rounding off to nearest thousands, 12904 rounds off to 13000 and 2888 rounds off to 3000

Estimated sum = 13000 + 3000 = 16000

(d) 28,292 - 21,496

By rounding off to nearest thousands, 28292 rounds off to 28000 and 21496 rounds off to 21000

Estimated difference= 28000 - 21000 = 7000

Exercise 1.3 Page Number 22

2

Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):

(a) 439 + 334 + 4317

(b) 1,08,734 – 47,599

(c) 8325 – 491

(d) 4,89,348 – 48,365

Answer

(a) 439 + 334 + 4317

Rounding off to nearest hundreds 439, 334 and 4317 may be rounded off to 400, 300 and 4300 respectively. 

 Estimated sum = 400 + 300 + 4300 = 5000

Rounding off to nearest tens, 439, 334 and 4317 may be rounded off to 440, 330 and 4320 respectively. 

Estimated sum = 440 + 330 + 4320 = 5090

(b) 1,08,734 – 47,599

Rounding off to nearest hundreds 1,08,734 and 47,559 may be rounded off to 1,08,700 and 47,600 respectively. 

Estimated difference = 1,08,700 - 47,600 = 61100

Rounding off to nearest tens 1,08,734 and 47,559 may be rounded off to 1,08,730 and 47,600 respectively.

Estimated difference = 1,08,730 - 47,600 = 61130

(c) 8325 – 491

Rounding off to nearest hundreds 8325 and 491 may be rounded off to 8300 and 500 respectively. 

Estimated difference = 8300 - 500 = 7800

Rounding off to nearest tens 8325 and 491 may be rounded off to 8330 and 490 respectively. 

Estimated difference = 8330 - 490 = 7840

(d) 4,89,348 – 48,365

Rounding off to nearest hundreds 4,89,348 and 48,365 may be rounded off to 4,89,300 and 48,400 respectively. 

Estimated difference = 489300 - 448400 = 440900

Rounding off to nearest tens 4,89,348 and 48,365 may be rounded off to 4,89,350 and 48,370 respectively. 

Estimated difference = 489350 - 48370 = 440980

Exercise 1.3 Page Number 22

3

Estimate the following products using general rule:

(a) 578 x 161

(b) 5281 x 3491

(c) 1291 x 592

(d) 9250 x 29

Answer

(a) 578 x 161

Rounding off by general rule, 578 and 161 may be rounded off to 600 and 200 respectively

The estimated product = 600 x 200 = 1,20,000

(b) 5281 x 3491

Rounding off by general rule, 5281 and 3491 may be rounded off to 5300 and 3500 respectively

The estimated product = 5,300 x 3,500 = 1,85,50,000

(c) 1291 x 592

Rounding off by general rule, 1291 and 592 may be rounded off to 1300 and 600 respectively

The estimated product = 1300 x 600 = 7,80,000

(d) 9250 x 29

Rounding off by general rule, 9250 and 29 may be rounded off to 9300 and 30 respectively

The estimated product = 9,300 x 30 = 2,79,000 

2,79,000 may be rounded off to 3,00,000

Exercise 1.3 Page Number 22

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